# Derivation of Bernoulli's Principle

## Main Question or Discussion Point

In my Fluid Mechanics textbook they use the Euler equation to derive Bernoulli's principle for incompressible fluids with gravity. In my earlier introduction to mechanics textbook they used energy conservation. Is there a reason for using the Euler equation or is it just to show more ways to derive Bernoulli's principle.
The reason I ask is because I find the Euler method more difficult.

I use Kundu/Cohen Fluid Mechanics

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well the origin in fluid mechanics theoris is NAVIER STOKES EQUATIONS as they cover all the conditions of the fluid as ( steady or unsteady ) comprissible or not , newtenion or not and bernollis equation is a special case of the navier stokes and so is eulers you can study this equation it will enable you to study many parameters pressure , time , velocity k, flow rate even power also

minger
As maxx mentioned Bernoulli's is derived from the full Navier-Stokes equations. Taking the full set of equations and ignoring viscosity you get the Euler equations.

Recall that these governing equations are based on Conservation of Mass, Momentum, and Energy. Those form a set of 5 coupled equations.

Bernoulli's is a special case basically of the energy equation. So, it is derived from Euler equation which is derived from conservation of energy.

edit: Perhaps you can show us the two different approaches. We might be able to help a little more knowing what you're looking at.

Thanks, then I will sit down and try to learn the cross-product rules.

Minger: the problem is my math knowledge.